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A050482 Sum of remainders when n-th prime is divided by all preceding integers. 3
0, 1, 4, 8, 22, 28, 51, 64, 98, 151, 167, 233, 297, 325, 403, 505, 635, 645, 790, 904, 923, 1113, 1244, 1422, 1654, 1800, 1888, 2056, 2098, 2256, 2849, 3066, 3326, 3450, 3969, 4045, 4329, 4696, 5014, 5325, 5767, 5759, 6499, 6565, 6898 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n)/(n*log(n))^2 appears to approach a constant ~0.22.. for large n. - Benedict W. J. Irwin, Dec 07 2016

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

a(n)= A004125(A000040(n)). [R. J. Mathar, Jun 12 2009]

EXAMPLE

a(4) = 8 because remainders when 7 is divided by 1..6 are 0,1,1,3,2,1, which add to 8.

a(2)=3 mod(3-1)=1. a(3) =(5 mod(5-1))+(5 mod(5-2))+(5 mod(5-3))=2+1+1=4.

MAPLE

A050482 := proc(n) local a, i; a := 0; for i from 1 to ithprime(n)-1 do a := a+(ithprime(n) mod i); od: end;

PROG

(PARI) a(n)=my(p=prime(n)); sum(k=2, p, p%k) \\ Charles R Greathouse IV, Jun 03 2013

CROSSREFS

Cf. A004125, A034953.

Sequence in context: A248423 A129794 A064503 * A200149 A153765 A003606

Adjacent sequences:  A050479 A050480 A050481 * A050483 A050484 A050485

KEYWORD

nonn

AUTHOR

Brian Wallace (wallacebrianedward(AT)yahoo.co.uk), Dec 26 1999

STATUS

approved

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Last modified March 29 13:11 EDT 2017. Contains 284270 sequences.